$12\mathrm{.}18)$ A $2\mathrm{.}00-$kg object is attached to a spring and placed on a frictionless, horizontal surface. A horizontal force of $20\mathrm{.}0$ N is required to hold the object at rest when it is pulled $0\mathrm{.}200$ m from its equilibrium position $($the origin of the x axis$).$ The object is now released from rest from this stretched position, and it subsequently undergoes simple harmonic oscillations. Find$($a$)$ the force constant of the spring, $($b$)$ the frequency of the oscillations, and $($c$)$ the maximum speed of the object. $($d$)$ Where does this maximum speed occur? $($e$)$ Find the maximum acceleration of the object.$($f$)$ Where does the maximum acceleration occur?$($g$)$ Find the total energy of the oscillating system. Find $($h$)$ the speed and $($i$)$ the acceleration of the object when its position is equal to one$-$third the maximum value.